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Magazine Problem 98
Is it possible to have no absolute minimum or maximum for a function? If so, construct such a function. If not, explain why this is not possible.
Problem 98
Draw a graph to support your explanation. Is it possible to have no absolute minimum or maximum for a function? If so, construct such a function. If not, explain why this is not possible.
Problem 104
Draw graphs of \(f(x),\) which is continuous, over the interval [-4,4] with the following properties: Absolute maximum at \(x=2\) and absolute minima at \(x=\pm 3\).
Problem 105
Draw graphs of \(f(x),\) which is continuous, over the interval [-4,4] with the following properties: Absolute minimum at \(x=1\) and absolute maximum at \(x=2\)
Problem 106
Draw graphs of \(f(x),\) which is continuous, over the interval [-4,4] with the following properties: Absolute maximum at \(x=4\), absolute minimum at \(x=-1,\) local maximum at \(x=-2,\) and a critical point that is not a maximum or minimum at \(x=2\)
Problem 107
Draw graphs of \(f(x),\) which is continuous, over the interval [-4,4] with the following properties: Absolute maxima at \(x=2\) and \(x=-3,\) local minimum at \(x=1\), and absolute minimum at \(x=4\)
Problem 108
For the following exercises, find the critical points in the domains of the following functions. $$y=4 x^{3}-3 x$$
Problem 108
Find the critical points in the domains of the following functions. \(y=4 x^{3}-3 x\)
Problem 109
Find the critical points in the domains of the following functions. \(y=4 \sqrt{x}-x^{2}\)
Problem 109
For the following exercises, find the critical points in the domains of the following functions. $$y=4 \sqrt{x}-x^{2}$$
